Partition

prtition.spad line 1 [edit on github]

Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus, (5 2 2 1) will represent s5 * s2^2 * s1.

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

0 : () -> %

from AbelianMonoid

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

coerce : % -> List(Integer)

coerce(p) coerces a partition into a list of integers

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

conjugate : % -> %

conjugate(p) returns the conjugate partition of a partition p

convert : % -> List(Integer)

from ConvertibleTo(List(Integer))

latex : % -> String

from SetCategory

max : (%, %) -> %

from OrderedSet

min : (%, %) -> %

from OrderedSet

opposite? : (%, %) -> Boolean

from AbelianMonoid

partition : List(Integer) -> %

partition(li) converts a list of integers li to a partition

pdct : % -> Integer

pdct(a1^n1 a2^n2 ...) returns n1! * a1^n1 * n2! * a2^n2 * .... This function is used in the package CycleIndicators.

powers : List(Integer) -> List(List(Integer))

powers(li) returns a list of 2-element lists. For each 2-element list, the first element is an entry of li and the second element is the multiplicity with which the first element occurs in li. There is a 2-element list for each value occurring in l.

sample : () -> %

from AbelianMonoid

smaller? : (%, %) -> Boolean

from Comparable

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

OrderedCancellationAbelianMonoid

CancellationAbelianMonoid

SetCategory

CoercibleTo(OutputForm)

OrderedAbelianMonoid

OrderedAbelianSemiGroup

AbelianMonoid

Comparable

OrderedSet

BasicType

AbelianSemiGroup

PartialOrder

ConvertibleTo(List(Integer))